A diving board has a perimeter of 22 feet and an area of 10 square feet. What are the dimensions of the diving board?

Answer 1

So, we must find the dimensions of the diving board such that

2l + 2w = 22

l*w = 10.............We modify the Area equation to yield l = 10 / w then plug it in such that

2(10/w) + 2w = 22.........Then

(20/w) + 2w = 22............Common denominator gives

(20+2w² / w) = 22............Then we cross multiply such that

20 + 2w² = 22w.............Then subtract 22w to the left side to get

2w² - 22w + 20...............Then we factor out a 2 to get

2(w² - 11w + 10) = 0................Then we factor the polynomial such that

(w-10)(w-1) = 0...............Then solve for w such that

w = 10 and w = 1............When we plug in 1 or 10, we get

l = 1 and 10.

So, the dimensions are w = 10 feet and l = 1 foot.

I hope this helped!

Answer 2

Greetings! Lets solve this shall we ?

So, we must find the dimensions of the diving board such that

2l + 2w = 22

l*w = 10.............We modify the Area equation to yield l = 10 / w then plug it in such that

2(10/w) + 2w = 22.........Then

(20/w) + 2w = 22............Common denominator gives

(20+2w² / w) = 22............Then we cross multiply such that

20 + 2w² = 22w.............Then subtract 22w to the left side to get

2w² - 22w + 20...............Then we factor out a 2 to get

2(w² - 11w + 10) = 0................Then we factor the polynomial such that

(w-10)(w-1) = 0...............Then solve for w such that

w = 10 and w = 1............When we plug in 1 or 10, we get

l = 1 and 10.

So, the dimensions are w = 10 feet and l = 1 foot.

I hope this helped!